Not much is known about Zatanna by most people, both in-universe and out of universe. This is perhaps appropriate. Zatanna is the official Mage of the JLA, due to the high versatility of her magic. She is equally at home performing magic tricks at kids’ parties and fighting magical threats to the universe.
Why is she so versatile? Well Zatanna herself represents the boundaries between two worlds. And I mean that in as many ways as possible. Zatanna exists in both DC (She is a premier member of the JLA) but also Vertigo (Her boyfriend is the most famous Vertigo Mage, John Constantine). She is the child of the two schools of magic in the DCU (learned and innate). She does fake magic as her job and real magic as her career. Zatanna as a character likes to inhabit the realm between two opposite realms.
This is because Zatanna loves the realm of possibility. Her form of power is manipulation over words, because words have the possibility to be anything. It’s also why she has her soft spot for children, because children represent infinite possibility, they could be good, they could be evil, they could be magical, they could be mundane, they could be understandable, they could be mysterious. It all depends how they develop.
The stories of Zatanna are really stories about understanding the intersections between opposed axioms and concepts, and that’s what makes her really fascinating to me. That and she is hot. :P